Convert $( 1 , - \sqrt { 3 } , \sqrt { 3 } )$ from rectangular coordinates to cylindrical coordinates.
A) $\left( 1 , \frac { \pi } { 3 } , \sqrt { 3 } \right)$
B) $\left( 1 , \frac { \pi } { 6 } , \sqrt { 3 } \right)$
C) $\left( \sqrt { 3 } , \frac { \pi } { 3 } , 1 \right)$
D) $\left( \sqrt { 3 } , \frac { \pi } { 6 } , 1 \right)$
E) $\left( 2 , \frac { \pi } { 3 } , \sqrt { 3 } \right)$
F) $\left( 2 , - \frac { \pi } { 3 } , \sqrt { 3 } \right)$
G) $\left( \sqrt { 3 } , \frac { \pi } { 3 } , 2 \right)$
H) $\left( \sqrt { 3 } , \frac { \pi } { 6 } , 2 \right)$

Question

Convert $( 1 , - \sqrt { 3 } , \sqrt { 3 } )$ from rectangular coordinates to cylindrical coordinates.
A) $\left( 1 , \frac { \pi } { 3 } , \sqrt { 3 } \right)$ 
B) $\left( 1 , \frac { \pi } { 6 } , \sqrt { 3 } \right)$ 
C) $\left( \sqrt { 3 } , \frac { \pi } { 3 } , 1 \right)$ 
D) $\left( \sqrt { 3 } , \frac { \pi } { 6 } , 1 \right)$ 
E) $\left( 2 , \frac { \pi } { 3 } , \sqrt { 3 } \right)$ 
F) $\left( 2 , - \frac { \pi } { 3 } , \sqrt { 3 } \right)$ 
G) $\left( \sqrt { 3 } , \frac { \pi } { 3 } , 2 \right)$ 
H) $\left( \sqrt { 3 } , \frac { \pi } { 6 } , 2 \right)$

Quizplus · Accepted Answer

The cylindrical coordinates are $(r, \theta, z)$. Here, $r = \sqrt{x^2 + y^2} = \sqrt{1^2 + (-\sqrt{3})^2} = 2$, $\theta = \tan^{-1}(y/x) = \tan^{-1}(-\sqrt{3}/1) = -\pi/3$, and $z = \sqrt{3}$.

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